### Punjabi University Patiala MCA Entrance Exam Syllabus

• English (Objective) : This paper will have questions from English Grammar such as choosing correct spellings, completion of sentences with suitable prepositions/articles, meaning of a word, synonym, antonym, meaning of idioms and phrases, choosing/ correcting grammatical errors in a part of given sentence, filling the blanks with correct form of verb, adjectives, adverbs etc. (Essay writing, Précis witting, unseen passage, for comprehension etc.)
• Mathematics
• UNIT-I
• NUMBER SYSTEM
1. Statements of the algebraic and order properties of the system of natural numbers, integers, rational numbers and real numbers and simple basic deductions from these properties.
2. The statements of the following results with illustrations but without proofs:
• Rational numbers as terminating decimals or as non-terminating recurring decimals, inadequacy of rationals.
• Irrational numbers as non-terminating, non-recurring decimals.
1. Representation of real numbers as points on a line, absolute value of real numbers.
• Complex numbers, representation of complex numbers, real and imaginary parts, modulus and argument of a complex number, conjugate of a complex number.
• Statements of the principle of mathematical induction in respect of natural number and simple application.
• TRIGONOMETRY
1. Angles and their measure in degrees and radians. Trigonometric function of angles of arbitrary magnitudes.
2. Addition formulae, sine, cosine and tangent of multiples and submultiples of angles. Periodicity and graph of sine, cosine and tangent functions.
3. Trigonometrical ratio of related angles.
4. Solution of simple trigonometric equations.
5. Sine and cosine formulae for triangles and simple cases of solution of triangles, problems on heights and distances.
• COORDINATE GEOMETRY
1. Distance formula and section formula.
2. Equation of line in a plane, general equation, equation of first degree, angle between two lines, parallel and perpendicular lines, distance of point from a line, family of lines.
3. Equation of a circle, general equation, equation of tangent and normal to a circle, radical axis of two circles.
4. Parametric representations of a circle.
5. Conic sections, equations of parabola, ellipse and hyperbola in standard form.
• COORDINATE GEOMETRY IN SPACE
1. Cartesian equations of lines and planes in three dimensions, angle between two lines, between a line and a plane and also between two planes, distance of a point from a plane, shortest distance between two lines, equations of any plane passing through the intersection of two planes.
2. Equation of a sphere, general equation.
• UNIT-II
• FUNCTIONS
1. Examples of real functions and their graphs.
2. Algebra of real functions, ex. of polynomial & rational functions.
3. One-one, on to and inverse functions.
1. Quadratic equations and their solutions, relationship between the roots and coefficients, formation of quadratic equations with given root, criteria for the nature of the roots of a quadratic equations.
2. Solution of quadratic in equations with their graphical representation.
• SEQUENCES AND SERIES
1. AP, GP and their sums.
• PERMUTATIONS, COMBINATIONS & THE BINOMIAL THEOREM
1. Elementary study of combinations, value of P and C, simple applications.
2. Binomial theorem for a positive integral index and its proof.
3. Statement of the binomial theorem for an arbitrary index & its application to approximations.
• UNIT-III
• MATRICES & DETERMINANTS
1. Determinants of square matrices of order not exceeding 3 and application to solutions of linear equations having a single solution. Cramer’s rule.
2. Sum and differences of matrices with not more than 3 rows & 3 columns.
3. Geometrical transformations (reflection, rotation, translation and enlargement) in a plane and their representation matrices, composite of reflections in two parallel lines and two intersecting lines.
4. Composition of transformations and products of matrices, non- commutativity of matrix multiplication, examples of non-zero matrices such that their product is zero matrix.
5. Non-singular matrices and their inverses, adjoint of a matrix.
6. Consistency of systems of two or three linear equations with two or three unknowns, linear equations in matrix notations, applications of matrices in solving simultaneous equations in three variables.
• CALCULUS
1. Notions of right handed and left handed limit and the limit and continuity of a function introduced through examples and illustrated graphically as well as numerically. Properties of continuous functions, continuity of polynomial, trigonometric, exponential and logarithmic functions.
2. Derivative of a function at a point, Derivative as instantaneous rate of change and slope of a curve. Tangents and normals.
3. Derivative of polynomial function.
4. Interpretation of the sign of the derivative at a point.
• UNIT-IV
• CALCULUS
1. Derivatives of quotients of functions and of rational functions.
2. Rolle’s Theorem illustrated geometrically, Derivations of the Lagrange’s Mean Value Theorem and its geometrical interpretation, Relation between the sign of derivative in an integral and monotonicity.
3. Determination of maximum and minimum values of a function. Graphs of polynomial functions of degree not exceeding 4.
4. Graphs and derivatives of trigonometric, inverse trigonometrical, exponential and logarithmic functions. Differentiation of implicit function, logarithmic differentiation, derivatives of functions expressed in parametric forms, derivative of higher order.
5. Primitives of functions and their calculations in simple cases.
6. Integration by substitution and by parts.
7. The definition of definite integral as the limit of a sum motivated by the determination of areas. Evaluation of definite integrals, properties of definite integrals.
8. Applications to determination of area under curves in simple differential cases. Differential Equations, order and degree, formation of a differential equation, general and particular solution of a differential equation, solution of a differential equation by the method of separable variables. Homogenous equation and their solution: Solution of the linear equation of the first order with constant coefficients.
• UNIT-V
• VECTORS
1. Vectors as a directed line segment, Addition of vectors, Multiplication of a vector by real number.
2. Position vector of a point. Section Formula.
3. Application of vectors of some geometrical results.
4. Scalar and vector product of two vector.
5. Scalar triple product, vector triple product.
• STATISTICS
1. Population and sample.
2. Measures of central tendency and dispersion.
3. Point and interval estimation (of mean only).
4. Scatter diagrams and Pearson’s correlation coefficient.
5. Calculation of the regression coefficient and the two lines of regression by the methods of least squares.
• PROBABILITY
1. Random experiments and sample space, events.
2. Probability on a discrete sample space, addition theorem.
3. Conditional probability, multiplication theorem
4. Independent events
5. Random variables (mean and variance. Calculations for simple probability distributions).
6. Normal distribution.
• Mental Ability : This paper will have the topics of logical reasoning, graphical analysis, analytical reasoning, and quantitative comparisons and series formation.

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